Many companies bootstrap their product development by providing services. You can do so from one company. At the point when you believe that the focus of the two businesses is a full time job each, and the channels for sales, etc. are not congruent, then you may want to consider spinning out the product company from the services company. You can even continue to do some services from your product company even, that are more in line with your product direction, and let the services company thrive on its own, at this point in time. It sounds like you're too early to worry about spinning out the product company from your services company. There are some accounting differences between the two types of businesses so that at some point, there may be positives from having two companies. As well, if there's conflicts not just in focus and accounting, but also in competitive issues with your product for your service customers, then the separation into two companies is of value.

Feel free to give me a call if you'd like to go through the details of your current situation in more detail.

Well you can always make the service company the parent company and the product company the subsidiary company or vice versa.

But honestly I don't see why you can't work everything under the same company name. Is there specific reasons you were given why not to do it? I have seen a lot of app development companies who do both under the same company name.